Question: The grades on a language midterm at Santa Rita are normally distributed with $\mu = 77$ and $\sigma = 3.5$. Tiffany earned a n $80$ on the exam. Find the z-score for Tiffany's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Tiffany's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{80 - {77}}{{3.5}}} $ ${ z \approx 0.86}$ The z-score is $0.86$. In other words, Tiffany's score was $0.86$ standard deviations above the mean.